Abstract
We investigate the issue of aggregativity in fair division problems from the perspective of cooperative game theory and Broomean theories of fairness. Paseau and Saunders (Utilitas 27:460–469, 2015) proved that no non-trivial theory of fairness can be aggregative and conclude that theories of fairness are therefore problematic, or at least incomplete. We observe that there are theories of fairness, particularly those that are based on cooperative game theory, that do not face the problem of non-aggregativity. We use this observation to argue that the universal claim that no non-trivial theory of fairness can guarantee aggregativity is false. Paseau and Saunders’s mistaken assertion can be understood as arising from a neglect of the (cooperative) games approach to fair division. Our treatment has two further pay-offs: for one, we give an accessible introduction to the (cooperative) games approach to fair division, whose significance has hitherto not been appreciated by philosophers working on fairness. For another, our discussion explores the issue of aggregativity in fair division problems in a comprehensive fashion.
Highlights
When our collective needs exceed the resources available, or when what is there is less than what is demanded, a fair division problem arises: how, in order to be fair, should a scarce good be divided? Take, for instance, the following fair division problem.Problem I John owes £80 to Ann and £40 to Bob but has only £60 left.How in order to be fair, must John divide the £60 that he has left between Ann and Bob? A popular answer, advocated for by John Broome (1990), is that John must divide the £60 proportional to the claims of Ann and Bob
We discussed the claims and games approach to fair division and explained that these approaches harbour theories of fairness that act on different fairness structures
We explained that whereas there are no aggregative theories of fairness on the claims approach, there are such theories on the games approach
Summary
When our collective needs exceed the resources available, or when what is there is less than what is demanded, a fair division problem arises: how, in order to be fair, should a scarce good be divided? Take, for instance, the following fair division problem. In a recent paper, Paseau and Saunders (2015) have argued that the aggregated allocation (70, 80) that results from applying the proportional rule to the above two problems is unfair. In a nutshell, their argument runs as follows. 4.1 we revisit Problem I and II both in terms of the RTB rule and the Shapley value and explain that certain conclusions with respect to these problems are an artefact from adopting the claims approach to fair division.
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